What is the general solution for 3cos(5t)=0 ?

The general solution for 3cos(5t)=0 is t= pi/(10)+(2pin)/5 ,t=(3pi}{10}+\frac{2pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cos(5t)=0

Solution

3 cos (5 t) = 0

Solution

t = \frac{π}{10} + \frac{2 πn}{5}, t = \frac{3 π}{10} + \frac{2 πn}{5}

Degrees

t = 1 8^{\circ} + 7 2^{\circ} n, t = 5 4^{\circ} + 7 2^{\circ} n

Solution steps

3 cos (5 t) = 0

Divide both sides by

3

3 cos (5 t) = 0

Divide both sides by

3

\frac{3 cos ( 5 t )}{3} = \frac{0}{3}

Simplify

cos (5 t) = 0

cos (5 t) = 0

General solutions for

cos (5 t) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

5 t = \frac{π}{2} + 2 πn, 5 t = \frac{3 π}{2} + 2 πn

5 t = \frac{π}{2} + 2 πn, 5 t = \frac{3 π}{2} + 2 πn

Solve

5 t = \frac{π}{2} + 2 πn : t = \frac{π}{10} + \frac{2 πn}{5}

5 t = \frac{π}{2} + 2 πn

Divide both sides by

5

5 t = \frac{π}{2} + 2 πn

Divide both sides by

5

\frac{5 t}{5} = \frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 t}{5} = \frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 t}{5} : t

\frac{5 t}{5}

Divide the numbers:

\frac{5}{5} = 1

= t

Simplify

\frac{\frac{π}{2}}{5} + \frac{2 πn}{5} : \frac{π}{10} + \frac{2 πn}{5}

\frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{2}}{5} = \frac{π}{10}

\frac{\frac{π}{2}}{5}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 5}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{π}{10}

= \frac{π}{10} + \frac{2 πn}{5}

t = \frac{π}{10} + \frac{2 πn}{5}

t = \frac{π}{10} + \frac{2 πn}{5}

t = \frac{π}{10} + \frac{2 πn}{5}

Solve

5 t = \frac{3 π}{2} + 2 πn : t = \frac{3 π}{10} + \frac{2 πn}{5}

5 t = \frac{3 π}{2} + 2 πn

Divide both sides by

5

5 t = \frac{3 π}{2} + 2 πn

Divide both sides by

5

\frac{5 t}{5} = \frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 t}{5} = \frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

Simplify

\frac{5 t}{5} : t

\frac{5 t}{5}

Divide the numbers:

\frac{5}{5} = 1

= t

Simplify

\frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5} : \frac{3 π}{10} + \frac{2 πn}{5}

\frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

\frac{\frac{3 π}{2}}{5} = \frac{3 π}{10}

\frac{\frac{3 π}{2}}{5}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{3 π}{2 \cdot 5}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{3 π}{10}

= \frac{3 π}{10} + \frac{2 πn}{5}

t = \frac{3 π}{10} + \frac{2 πn}{5}

t = \frac{3 π}{10} + \frac{2 πn}{5}

t = \frac{3 π}{10} + \frac{2 πn}{5}

t = \frac{π}{10} + \frac{2 πn}{5}, t = \frac{3 π}{10} + \frac{2 πn}{5}

Popular Examples

cos^2(90-θ)=1872

cos^{2} (9 0^{\circ} - θ) = 1872

cos(x)-sqrt(cos(x))=0

cos (x) - cos (x) = 0

sin(x+1)=cos(x)

sin (x + 1) = cos (x)

3cos(x)-2=1

3 cos (x) - 2 = 1

sin(4x)=-sin(2x)

sin (4 x) = - sin (2 x)

Frequently Asked Questions (FAQ)

What is the general solution for 3cos(5t)=0 ?
The general solution for 3cos(5t)=0 is t= pi/(10)+(2pin)/5 ,t=(3pi}{10}+\frac{2pin)/5